Descriptive set theory | Topology
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets). Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some contexts, Borel sets are defined to be generated by the compact sets of the topological space, rather than the open sets. The two definitions are equivalent for many well-behaved spaces, including all Hausdorff σ-compact spaces, but can be different in more pathological spaces. (Wikipedia).
Stirring the Mandelbrot Set: a checkerboard
http://code.google.com/p/mandelstir/
From playlist mandelstir
Fractal Moonlight Sonata Just more fractals and even more Beethoven. Eventually all these could be put into some sort of playlist. Maybe. Who knows! #Beethoven #Fractal
From playlist Nerdy Rodent Uploads!
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
The Mandelbrot set is a churning machine
Its job is to fling off the red pixels and hang onto the green ones. Audio by @Dorfmandesign
From playlist mandelstir
The Mandelbrot set is a complex fractal, arguably one of the most beautiful structures in mathematics. It is introduced in this video.
From playlist Fun
(PP 1.8) Measure theory: CDFs and Borel Probability Measures
Correspondence between Borel probability measures on R and CDFs (cumulative distribution functions). A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4 You can skip the measure theory (Section 1) if you're not in
From playlist Probability Theory
Semantic models for higher-order Bayesian inference - Sam Staton, University of Oxford
In this talk I will discuss probabilistic programming as a method of Bayesian modelling and inference, with a focus on fully featured probabilistic programming languages with higher order functions, soft constraints, and continuous distributions. These languages are pushing the limits of e
From playlist Logic and learning workshop
Natasha Dobrinen: Borel sets of Rado graphs are Ramsey
The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint fr
From playlist Combinatorics
Introduction to Resurgence, Trans-series and Non-perturbative Physics - I by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
(PP 1.S) Measure theory: Summary
A brief summary of the material from this section, emphasizing probability measures.
From playlist Probability Theory
Présentation de l'exposition "Emile Borel : un mathématicien au pluriel"
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From playlist Bibliothèque
Stavros Garoufalidis - Arithmetic Resurgence of Quantum Invariants
I will explain some conjectures concerning arithmetic resurgence of quantum knot and 3-manifold invariants formulated in an earlier work of mine in 2008, as well as numerical tests of those conjectures and their relations to quantum modular forms, state integrals and their q-series. Joint
From playlist Resurgence in Mathematics and Physics
(PP 3.1) Random Variables - Definition and CDF
(0:00) Intuitive examples. (1:25) Definition of a random variable. (6:10) CDF of a random variable. (8:28) Distribution of a random variable. A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4
From playlist Probability Theory
The general rational laws of trigonometry | WildTrig: Intro to Rational Trigonometry
We establish the laws of rational trigonometry in the very general planar setting of having a general bilinear form which determines the notions of quadrance and spread. Pleasantly the laws of RT are still the familiar ones, but the interest is in seeing just how elegantly and simply these
From playlist WildTrig: Intro to Rational Trigonometry